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Byju's Answer
Standard XII
Mathematics
Monotonically Increasing Functions
Given that ...
Question
Given that
cos
h
x
=
5
4
, determine the values of
sin
h
x
Use the formula for
cos
h
(
2
x
+
x
)
to determine the value of
cos
h
3
x
.
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Solution
we have,
cos
h
x
=
5
4
e
x
+
e
−
x
2
=
5
4
4
e
2
x
−
10
e
x
+
4
=
0
e
x
=
10
+
−
√
100
−
64
8
e
x
=
2
or
1
2
now,
sin
h
x
=
3
4
or
−
3
4
here we have to calculate
cos
3
h
x
by spliting that into
cos
h
(
2
x
+
x
)
cos
h
2
x
=
2
(
cos
h
x
)
2
−
1
cos
h
2
x
=
17
8
sin
h
2
x
=
2
cos
h
x
sin
h
x
sin
2
h
x
=
15
8
or
−
15
8
cos
h
3
x
=
cos
h
(
2
x
+
x
)
=
cos
h
2
x
cos
h
x
+
sin
h
2
x
sin
h
x
cos
3
h
x
=
40
32
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0
Similar questions
Q.
Given that
cos
h
x
=
5
4
, determine the values of
cos
h
2
x
Use the formula for
cos
h
(
2
x
+
x
)
to determine the value of
cos
h
3
x
.
Q.
Given that
sin
h
x
=
5
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, find the values of
cos
h
2
x
Determine the value of
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as a natural logarithm
Q.
Given that
sin
h
x
=
5
12
, find the values of
cos
h
x
Determine the value of
x
as a natural logarithm
Q.
Use the definitions of
sin
h
x
and
cos
h
x
in terms of exponential functions to prove that
cos
h
2
x
=
cos
h
2
x
−
1
Q.
Show that
cos
h
x
+
sin
h
x
=
e
x
and simplify
cos
h
x
−
sin
h
x
=
?
.
By considering
(
cos
h
x
+
sin
h
x
)
2
+
(
cos
h
x
−
sin
h
x
)
2
show that
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x
−
sin
2
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x
=
cos
h
2
x
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